Abstract

While investigating the instrumental function of a Fabry–Perot interferometer [Appl. Opt. 34, 58 (1995)], we noticed some variation in finesse and contrast in the measured spectra when a 1.5-mm-diameter aperture was used at various spots within the standard 8-mm aperture. By comparing experimentally determined finesse versus contrast plots for many such spectra with calculated plots, we found spots on the plates that gave non-Airy-function line shapes over the entire order of interference, unlike the Airy line shape we determined previously by using the entire 8-mm aperture. We have reviewed several models that describe the effects of various types of surface defects, such as Gaussian-height distribution of roughness, curvature and tilt of plates, sinusoidal roughness, and asymmetrical roughness on the finesse and contrast. Our experimental results can be accounted for if we assume that the reflectivity is nonuniform over the Fabry–Perot plates and that there is some reasonable contribution that is due to Gaussian roughness, curvature, or tilt.

J. R. Sandercock, “The design and use of a stabilized multipassed interferometer of high contrast ratio,” in Proceedings of the Second International Conference on Light Scattering in Solids, M. Balkanski, ed. (Flammarion, Paris, 1971), p. 9.

Sainty, W. G.

Sandercock, J. R.

J. R. Sandercock, “The design and use of a stabilized multipassed interferometer of high contrast ratio,” in Proceedings of the Second International Conference on Light Scattering in Solids, M. Balkanski, ed. (Flammarion, Paris, 1971), p. 9.

Other (10)

J. R. Sandercock, “The design and use of a stabilized multipassed interferometer of high contrast ratio,” in Proceedings of the Second International Conference on Light Scattering in Solids, M. Balkanski, ed. (Flammarion, Paris, 1971), p. 9.

(a) Calculated contrast C plotted as a function of calculated finesse ℱ for an Airy function with a range of values of R from 0.94 to 0.30. If defects of Gaussian roughness are introduced for various values of parameter λ/mG, the grid shown is obtained. For curvature defects only, some values of mC, are shown and a corresponding grid can be inferred. (b) Measured contrast is plotted as a function of measured finesse. Similar points indicate data derived from 1-pass spectra taken the same day but at different 1.5-mm-diameter spots on the plates. To give some estimate of the variations of R and curvature or Gaussian roughness over the plates, we show C versus ℱ curves derived for ideal FP plates (solid curve) and FP plates with defects (dashed curve).

Experimental 1-pass spectrum fitted over one order of interference (FSR) with the defect model discussed in the text, mG = mT= mC = 20,000, R = 0.910. From the calculated fit we find ℱ = 33.3, C = 453. The two sets of data points are from spectra obtained with (●) and without (○) the filters, which emphasize the maximum and the minimum, respectively. Count-rate statistics (normalized) are indicated by a few vertical bars at that level of count rate. (b) Experimental 1-pass spectrum taken at a different spot from that of (a) is fitted with mG = mT = 20,000, R = 0.919 but with mC = 120. From the calculated fit we find ℱ = 31.6 and C = 502. (c) Experimental 1-pass spectrum fitted with mG = mT = 20,000, R = 0.937, and mC = 100. From the calculated fit we find ℱ = 34.7, C = 732.

(a) Calculated 1-pass contrast C1 is plotted as a function of calculated finesse ℱ1 for 0.84 ≤ R ≤ 0.93 (solid curve). When curvature is added at R = 0.91, for example, the contrast and the finesse are degraded, as shown by the dashed curve. The experimental data listed in Table 1 are plotted: our experimental 1-pass datum point (Δ), the 1-pass experimental (or inferred) data points of Durvasula and Gammon40 (●), Vaughan41 (□), Lindsay and Shepherd42 (∇), our measured datum point for a second interferometer (○). (b) Calculated 3-pass contrast C3 is plotted as a function of calculated finesse ℱ3 (solid curve). When curvature is added at R = 0.91, the contrast and the finesse are degraded, as shown by the dashed curve. Experimental 3-pass data points listed in Table 1 are plotted; the data points are identified in the caption of (a). (c) Calculated 5-pass contrast C5 is plotted as a function of calculated finesse ℱ5 (solid curve). When curvature is added at R = 0.91, the contrast and the finesse are degraded, as shown by the dashed curve. Experimental 5-pass data points listed in Table 1 are plotted: Sandercock43 (□) and Dil and Brody44 (Δ), (∇).

a The experimental data are plotted in Fig. 4. The data in the 1-pass (calc) and 1-pass (exp) columns for Ref. 4 are identical because the (Exp) spectrum was fit to acquire the (calc) spectrum.b Values inferred from the 3-pass (exp) data by the use of Eqs. (4) and (5).c The 1-pass (calc) and 3-pass (calc) columns for Ref. 41 were obtained assuming that R = 0.885.d The subcolumns in the 1-pass (calc) and 3-pass (calc) columns for Ref. 40 arise from our assumption that R is significantly less that the vendor-specified value of 0.94.